Properties of Exponents and Radicals

Find all fourth roots of 256.

• 4, -4

• 64, -64

• 8, -8

• 16, -16

Find all cube roots of -125.

• 3

• -3

• 5

• -5

• No Solution

Write each expression in radical form.
 $\left(6k\right)^{\frac{5}{2}}$  

•  $6\sqrt{k^5}$  

•  $6\sqrt{k^2}$  

•  $\sqrt{6k^5}$  

•  $\sqrt{\left(6k\right)^5}$  

Write each expression in exponential form.
 $\frac{1}{\left(\sqrt{5p}\right)^3}$  

•  $\left(5p\right)^{-\frac{3}{2}}$  

•  $5p^{-\frac{3}{2}}$  

•  $\left(5p\right)^{-3}$  

•  $\left(5p\right)^3$  

Simplify. Use absolute value signs when necessary.
 $\sqrt{147x}$  

•  $6\sqrt{7x}$  

•  $7\sqrt{3x}$  

•  $6\sqrt{2x}$  

•  $3\sqrt{7x}$  

Simplify. Use absolute value signs when necessary. $-3\sqrt{75a^3b^4}$  

•  $30b^2\left|a\right|\sqrt{2a}$  

•  $-6b^2\left|a\right|$  

•  $-12b^2\left|a\right|\sqrt{3}$  

•  $-15b^2\left|a\right|\sqrt{3a}$  

Simplify $\sqrt{180r^4}$  

•  $6r^2\sqrt{5}$  

•  $3r\sqrt{20r}$  

•  $36r^2\sqrt{5}$  

•  $9r\sqrt{20r}$  

Simplify. Your answer should contain only positive exponents.

 $x^3y^{-1}\cdot2y^2$  

•  $4x^3y^{ }$  

•  $2x^3y^{ }$  

•  $\frac{4x^3}{y^2}$  

•  $\frac{2x^3}{y^2}$  

Simplify. Your answer should contain only positive exponents.

 $\left(a^3b^4\right)^3$  

•  $a^6b^7$  

•  $a^9b^{12}$  

•  $3a^3b^4$  

•  $b^{12}$  

Simplify. Your answer should contain only positive exponents.

 $\frac{y^3}{x^{-3}y^{-1}}$  

•  $x^3y^3$  

•  $x^3y^4$  

•  $x^3y^2$  

•  $x^{-3}y^{-3}$